Challenging the traditional sequence of teaching introductory calculus

Herbert, Sandra 2013, Challenging the traditional sequence of teaching introductory calculus, Computers in the schools : interdisciplinary journal of practice, theory, and applied research, vol. 30, no. 1-2, pp. 172-190, doi: 10.1080/07380569.2013.771528.

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Title Challenging the traditional sequence of teaching introductory calculus
Author(s) Herbert, SandraORCID iD for Herbert, Sandra
Journal name Computers in the schools : interdisciplinary journal of practice, theory, and applied research
Volume number 30
Issue number 1-2
Start page 172
End page 190
Total pages 19
Publisher Taylor & Francis
Place of publication Abingdon, England
Publication date 2013-06
ISSN 0738-0569
Keyword(s) calculus
multiple representations
Summary Despite considerable research with students of calculus, rate, and hence derivative, remain difficult concepts to teach and learn. The demonstrated lack of conceptual understanding of introductory calculus limits its usefulness in related areas. Since rate is such a troublesome concept, this study piloted reversing the usual presentation of introductory calculus to begin with area and integration, rather than rate and derivative. Two classes of first-year university students taking introductory calculus were selected to pilot the effect of changing the sequence; one class was a control group and the other class followed the reversed sequence. Advances in technology, especially computer algebra systems (CASs) may facilitate new ways of studying mathematics. In this study, handheld CASs were used to support students’ thinking as they grappled with the concepts of introductory calculus. The use of CASs enabled consideration of symbolic patterns and numerical integration leading to a deeper conceptual understanding of integration. The easy access to the multiple representations of functions provided by CASs facilitated an exploration of rate where each representation highlighted different aspects of rate resulting in deeper conceptual understanding of differentiation.
Language eng
DOI 10.1080/07380569.2013.771528
Field of Research 130208 Mathematics and Numeracy Curriculum and Pedagogy
Socio Economic Objective 930302 Syllabus and Curriculum Development
HERDC Research category C1 Refereed article in a scholarly journal
Copyright notice ©2013, Taylor & Francis
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Document type: Journal Article
Collections: Faculty of Arts and Education
School of Education
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Created: Wed, 17 Jul 2013, 15:07:27 EST by Sandra Herbert

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